If, $\vec a,\vec b,\vec c,\vec d$ are any four vectors, then $(\vec a×\vec b) × (\vec c×\vec d)$ is a vector
Answer & explanation
Correct answer: option 2
Clearly $\vec a×\vec b$ is perpendicular to the plane containing $\vec a$ and $\vec b$.
Also, $\vec c×\vec d$ is perpendicular to the plane containing $\vec c$ and $\vec d$.
Therefore, $(\vec a×\vec b) × (\vec c×\vec d)$ is along the line of intersection of the planes determined by $\vec a$ and $\vec b$ and the other determined by $\vec c$ and $\vec d$.